GATE ME: Engineering Mechanics Champion Quiz 5

A swimmer can swim 10 km in 2 hours when swimming along the flow of a river, While swimming against the flow. She takes 5 hours for the same distance. Her speed in still water (in km/h) is _______

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is _________

A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30 ° with the vertical. The magnitude of force F (in N) is __________

A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in the figure, where the wrapping angle is 180 °. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in N.m is

An ejector mechanism consists of a helical compression spring having a spring constant of K = 981 × 10³ N/m. it is pre-compressed by 100 mm from its free state. If it is used to eject a mass of 100 kg held on it, the mass will move up through a distance of

The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following expression:
a = -0.1v,
where v is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be ____